On the Harnack inequality for quasilinear elliptic equations with a first-order term

We consider weak solutions to −∆pu + a(x, u)|∇u|q = f(x, u), with p > 1, q ≥ max{p − 1, 1}. We exploit the Moser iteration technique to prove a Harnack comparison inequality for C 1 weak solutions. As a consequence we deduce a strong comparison principle.